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Moir\'{e} twist angle underpins the interlayer interaction of excitons in twisted van der Waals hetero- and homo-structures. The influence of twist angle on the excitonic absorption of twisted bilayer tungsten diselenide (WSe$_{2}$) has been investigated using electron energy-loss spectroscopy. Atomic-resolution imaging by scanning transmission electron microscopy was used to determine key structural parameters, including the nanoscale measurement of the relative twist angle and stacking order. Detailed spectral analysis revealed a pronounced blueshift in the high-energy excitonic peak C with increasing twist angle, up to 200 meV when compared to the AA$^{\prime}$ stacking. The experimental findings have been discussed relative to first-principle calculations of the dielectric response of the AA$^{\prime}$ stacked bilayer WSe$_{2}$ as compared to monolayer WSe$_{2}$ by employing the \textit{GW} plus Bethe-Salpeter equation (BSE) approaches, resolving the origin of higher energy spectral features from ensembles of excitonic transitions, and thus any discrepancies between previous calculations. Furthermore, the electronic structure of moir\'{e} supercells spanning twist angles of $\sim$9.5-46.5$^{\circ}$ calculated by density functional theory (DFT) were unfolded, showing an uplifting of the conduction band minimum near the $Q$ point and minimal change in the upper valence band concurrently. The combined experiment/theory investigation provides valuable insight into the physical origins of high-energy absorption resonances in twisted bilayers, which enables to track the evolution of interlayer coupling from tuning of the exciton C transitions by absorption spectroscopy.

We present a Faraday rotation spectroscopy (FRS) technique for measurements on the micron scale. Spectral acquisition speeds of many orders of magnitude faster than state-of-the-art modulation spectroscopy setups are demonstrated. The experimental method is based on charge-coupled-device detection, avoiding speed-limiting components, such as polarization modulators with lock-in amplifiers. At the same time, FRS spectra are obtained with a sensitivity of 20 $\mu$rad (0.001$^\circ$) over a broad spectral range (525 nm - 800 nm), which is on par with state-of-the-art polarization-modulation techniques. The new measurement technique also automatically cancels unwanted Faraday rotation backgrounds. Using the setup, we perform Faraday rotation spectroscopy of excitons in a hBN-encapsulated atomically thin semiconductor WS$_2$ under magnetic fields of up to 1.4 T at room temperature and liquid helium temperature. We determine the A exciton g-factor of -4.4 $\pm$ 0.3 at room temperature, and -4.2 $\pm$ 0.2 at liquid helium temperature. In addition, we perform FRS and hysteresis loop measurements on a 20 nm thick film of an amorphous magnetic Tb$_{0.2}$Fe$_{0.8}$ alloy., Comment: 8 pages, 4 figures

We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{ab-initio}$ calculations and quantitatively explain the optical response of doped monolayers with temperature., Comment: 16 pages including supporting information, 4 figures in the main text, 10 figures in the supporting information

Here, we propose a method to determine the thickness of the most common transition metal dichalcogenides (TMDCs) placed on the surface of transparent stamps, used for the deterministic placement of two-dimensional materials, by analyzing the red, green and blue channels of transmission-mode optical microscopy images of the samples. In particular, the blue channel transmittance shows a large and monotonic thickness dependence, making it a very convenient probe of the flake thickness. The method proved to be robust given the small flake-to-flake variation and the insensitivity to doping changes of MoS2. We also tested the method for MoSe2, WS2 and WSe2. These results provide a reference guide to identify the number of layers of this family of materials on transparent substrates only using optical microscopy., Comment: 4 figures in main text, 2 figures in supp. info

The research field of two dimensional (2D) materials strongly relies on optical microscopy characterization tools to identify atomically thin materials and to determine their number of layers. Moreover, optical microscopy-based techniques opened the door to study the optical properties of these nanomaterials. We presented a comprehensive study of the differential reflectance spectra of 2D semiconducting transition metal dichalcogenides (TMDCs), MoS2, MoSe2, WS2, and WSe2, with thickness ranging from one layer up to six layers. We analyzed the thickness-dependent energy of the different excitonic features, indicating the change in the band structure of the different TMDC materials with the number of layers. Our work provided a route to employ differential reflectance spectroscopy for determining the number of layers of MoS2, MoSe2, WS2, and WSe2., Comment: Main text (3 Figures) and Supp. Info. (23 Figures)

Strain engineering in single-layer semiconducting transition metal dichalcogenides aims to tune their bandgap energy and to modify their optoelectronic properties by the application of external strain. In this paper we study transition metal dichalcogenides monolayers deposited on polymeric substrates under the application of biaxial strain, both tensile and compressive. We can control the amount of biaxial strain applied by letting the substrate thermally expand or compress by changing the substrate temperature. After modelling the substrate-dependent strain transfer process with a finite elements simulation, we performed micro-differential spectroscopy of four transition metal dichalcogenides monolayers (MoS2, MoSe2, WS2, WSe2) under the application of biaxial strain and measured their optical properties. For tensile strain we observe a redshift of the bandgap that reaches a value as large as 94 meV/% in the case of single-layer WS2 deposited on polypropylene. The observed bandgap shifts as a function of substrate extension/compression follow the order WS2 > WSe2 > MoS2 > MoSe2., Comment: 13 pages, 5 figures

Tungsten diselenide (WSe2), a semiconducting transition metal dichalcogenide (TMDC), shows great potential as active material in optoelectronic devices due to its ambipolarity and direct bandgap in its single-layer form. Recently, different groups have exploited the ambipolarity of WSe2 to realize electrically tunable PN junctions, demonstrating its potential for digital electronics and solar cell applications. In this Letter, we focus on the different photocurrent generation mechanisms in a double-gated WSe2 device by measuring the photocurrent (and photovoltage) as the local gate voltages are varied independently in combination with above- and below-bandgap illumination. This enables us to distinguish between two main photocurrent generation mechanisms: the photovoltaic and photothermoelectric effect. We find that the dominant mechanism depends on the defined gate configuration. In the PN and NP configurations, photocurrent is mainly generated by the photovoltaic effect and the device displays a maximum responsivity of 0.70 mA/W at 532 nm illumination and rise and fall times close to 10 ms. Photocurrent generated by the photothermoelectric effect emerges in the PP configuration and is a factor of two larger than the current generated by the photovoltaic effect (in PN and NP configurations). This demonstrates that the photothermoelectric effect can play a significant role in devices based on WSe2 where a region of strong optical absorption, caused by e.g. an asymmetry in flake thickness or optical absorption of the electrodes, generates a sizeable thermal gradient upon illumination., Comment: Main text (4 figures) + Supp. Info. (11 figures)